Abstract: In 2007, Roberts and Schmidt had a satisfactory local new- and oldform theory for $GSp(4)$ with trivial central character, in which they considered the vectors fixed by the paramodular groups $K(p^n)$. In this talk, we consider the vectors fixed by the Klingen subgroup of level $p^2$. We determine the dimensions of the spaces of these invariant vectors for all irreducible, admissible representations of $GSp(4)$ over a $p$-adic field.
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